Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+6y &= 3 \\ -2x+2y &= 4\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = -2y+4$ Divide both sides by $-2$ to isolate $x$ $x = {y - 2}$ Substitute this expression for $x$ in the first equation. $4({y - 2}) + 6y = 3$ $4y - 8 + 6y = 3$ Simplify by combining terms, then solve for $y$ $10y - 8 = 3$ $10y = 11$ $y = \dfrac{11}{10}$ Substitute $\dfrac{11}{10}$ for $y$ in the top equation. $4x+6( \dfrac{11}{10}) = 3$ $4x+\dfrac{33}{5} = 3$ $4x = -\dfrac{18}{5}$ $x = -\dfrac{9}{10}$ The solution is $\enspace x = -\dfrac{9}{10}, \enspace y = \dfrac{11}{10}$.